   # What is the domain of z = 3 x + 2 y x 2 + y 2 ? ### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781337625340

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781337625340
Chapter 14, Problem 2RE
Textbook Problem
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## What is the domain of z = 3 x + 2 y x 2 + y 2 ?

To determine

To calculate: The domain of the function z=3x+2yx2+y2.

### Explanation of Solution

Given Information:

The provided function is z=3x+2yx2+y2.

Formula used:

The domain of a function of two variables f(x,y) is the set of all ordered pairs (x,y) for which the function is well-defined.

If the function maps each element of the domain to an element in the codomain, then it is said to be well defined.

To find the domain of a rational function, set the denominator of the function equals to zero. Then the domain of the function is the set of all ordered pairs except the values for which the denominator is zero.

The function f(x)=x is defined for all x0.

Calculation:

Consider the provided function, z=3x+2yx2+y2.

Rewrite z as f(x,y) in f(x,y)=3x+2yx2+y2.

Thus,

f(x,y)=3x+2yx2+y2

The function f(x,y) is a rational function.

Recall that, to find the domain of a rational function, set the denominator of the function equals to zero. Then the domain of the function is the set of all ordered pairs except the values for which the denominator is zero

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